The arithmetic-geometric scaling spectrum for continued fractions

To compare continued fraction digits with the denominators of the corresponding approximants we introduce the arithmetic-geometric scaling. We will completely determine its multifractal spectrum by means of a number theoretical free energy function and show that the Hausdorff dimension of sets consisting of irrationals with the same scaling exponent coincides with the Legendre transform of this free energy function. Furthermore, we identify the asymptotic of the local behaviour of the spectrum at the right boundary point and discuss a connection to the set of irrationals with continued fraction digits exceeding a given number which tends to infinity.Comment: 22 pages, 1 figur

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts

Pan-cancer Alterations of the MYC Oncogene and Its Proximal Network across the Cancer Genome Atlas

Although theMYConcogene has been implicated incancer, a systematic assessment of alterations ofMYC, related transcription factors, and co-regulatoryproteins, forming the proximal MYC network (PMN),across human cancers is lacking. Using computa-tional approaches, we define genomic and proteo-mic features associated with MYC and the PMNacross the 33 cancers of The Cancer Genome Atlas.Pan-cancer, 28% of all samples had at least one ofthe MYC paralogs amplified. In contrast, the MYCantagonists MGA and MNT were the most frequentlymutated or deleted members, proposing a roleas tumor suppressors.MYCalterations were mutu-ally exclusive withPIK3CA,PTEN,APC,orBRAFalterations, suggesting that MYC is a distinct onco-genic driver. Expression analysis revealed MYC-associated pathways in tumor subtypes, such asimmune response and growth factor signaling; chro-matin, translation, and DNA replication/repair wereconserved pan-cancer. This analysis reveals insightsinto MYC biology and is a reference for biomarkersand therapeutics for cancers with alterations ofMYC or the PMN

Spatial Organization and Molecular Correlation of Tumor-Infiltrating Lymphocytes Using Deep Learning on Pathology Images

Beyond sample curation and basic pathologic characterization, the digitized H&E-stained images of TCGA samples remain underutilized. To highlight this resource, we present mappings of tumorinfiltrating lymphocytes (TILs) based on H&E images from 13 TCGA tumor types. These TIL maps are derived through computational staining using a convolutional neural network trained to classify patches of images. Affinity propagation revealed local spatial structure in TIL patterns and correlation with overall survival. TIL map structural patterns were grouped using standard histopathological parameters. These patterns are enriched in particular T cell subpopulations derived from molecular measures. TIL densities and spatial structure were differentially enriched among tumor types, immune subtypes, and tumor molecular subtypes, implying that spatial infiltrate state could reflect particular tumor cell aberration states. Obtaining spatial lymphocytic patterns linked to the rich genomic characterization of TCGA samples demonstrates one use for the TCGA image archives with insights into the tumor-immune microenvironment

Selective redox regulation of cytokine receptor signaling by extracellular thioredoxin-1

The thiol-disulfide oxidoreductase thioredoxin-1 (Trx1) is known to be secreted by leukocytes and to exhibit cytokine-like properties. Extracellular effects of Trx1 require a functional active site, suggesting a redox-based mechanism of action. However, specific cell surface proteins and pathways coupling extracellular Trx1 redox activity to cellular responses have not been identified so far. Using a mechanism-based kinetic trapping technique to identify disulfide exchange interactions on the intact surface of living lymphocytes, we found that Trx1 catalytically interacts with a single principal target protein. This target protein was identified as the tumor necrosis factor receptor superfamily member 8 (TNFRSF8/CD30). We demonstrate that the redox interaction is highly specific for both Trx1 and CD30 and that the redox state of CD30 determines its ability to engage the cognate ligand and transduce signals. Furthermore, we confirm that Trx1 affects CD30-dependent changes in lymphocyte effector function. Thus, we conclude that receptor–ligand signaling interactions can be selectively regulated by an extracellular redox catalyst

Comprehensive molecular characterization of gastric adenocarcinoma

Gastric cancer is a leading cause of cancer deaths, but analysis of its molecular and clinical characteristics has been complicated by histological and aetiological heterogeneity. Here we describe a comprehensive molecular evaluation of 295 primary gastric adenocarcinomas as part of The Cancer Genome Atlas (TCGA) project. We propose a molecular classification dividing gastric cancer into four subtypes: tumours positive for Epstein–Barr virus, which display recurrent PIK3CA mutations, extreme DNA hypermethylation, and amplification of JAK2, CD274 (also known as PD-L1) and PDCD1LG2 (also knownasPD-L2); microsatellite unstable tumours, which show elevated mutation rates, including mutations of genes encoding targetable oncogenic signalling proteins; genomically stable tumours, which are enriched for the diffuse histological variant and mutations of RHOA or fusions involving RHO-family GTPase-activating proteins; and tumours with chromosomal instability, which show marked aneuploidy and focal amplification of receptor tyrosine kinases. Identification of these subtypes provides a roadmap for patient stratification and trials of targeted therapies

Comprehensive Pan-Genomic Characterization of Adrenocortical Carcinoma

SummaryWe describe a comprehensive genomic characterization of adrenocortical carcinoma (ACC). Using this dataset, we expand the catalogue of known ACC driver genes to include PRKAR1A, RPL22, TERF2, CCNE1, and NF1. Genome wide DNA copy-number analysis revealed frequent occurrence of massive DNA loss followed by whole-genome doubling (WGD), which was associated with aggressive clinical course, suggesting WGD is a hallmark of disease progression. Corroborating this hypothesis were increased TERT expression, decreased telomere length, and activation of cell-cycle programs. Integrated subtype analysis identified three ACC subtypes with distinct clinical outcome and molecular alterations which could be captured by a 68-CpG probe DNA-methylation signature, proposing a strategy for clinical stratification of patients based on molecular markers

Integrated genomic characterization of oesophageal carcinoma

Oesophageal cancers are prominent worldwide; however, there are few targeted therapies and survival rates for these cancers remain dismal. Here we performed a comprehensive molecular analysis of 164 carcinomas of the oesophagus derived from Western and Eastern populations. Beyond known histopathological and epidemiologic distinctions, molecular features differentiated oesophageal squamous cell carcinomas from oesophageal adenocarcinomas. Oesophageal squamous cell carcinomas resembled squamous carcinomas of other organs more than they did oesophageal adenocarcinomas. Our analyses identified three molecular subclasses of oesophageal squamous cell carcinomas, but none showed evidence for an aetiological role of human papillomavirus. Squamous cell carcinomas showed frequent genomic amplifications of CCND1 and SOX2 and/or TP63, whereas ERBB2, VEGFA and GATA4 and GATA6 were more commonly amplified in adenocarcinomas. Oesophageal adenocarcinomas strongly resembled the chromosomally unstable variant of gastric adenocarcinoma, suggesting that these cancers could be considered a single disease entity. However, some molecular features, including DNA hypermethylation, occurred disproportionally in oesophageal adenocarcinomas. These data provide a framework to facilitate more rational categorization of these tumours and a foundation for new therapies

Multiple novel prostate cancer susceptibility signals identified by fine-mapping of known risk loci among Europeans

Genome-wide association studies (GWAS) have identified numerous common prostate cancer (PrCa) susceptibility loci. We have fine-mapped 64 GWAS regions known at the conclusion of the iCOGS study using large-scale genotyping and imputation in 25 723 PrCa cases and 26 274 controls of European ancestry. We detected evidence for multiple independent signals at 16 regions, 12 of which contained additional newly identified significant associations. A single signal comprising a spectrum of correlated variation was observed at 39 regions; 35 of which are now described by a novel more significantly associated lead SNP, while the originally reported variant remained as the lead SNP only in 4 regions. We also confirmed two association signals in Europeans that had been previously reported only in East-Asian GWAS. Based on statistical evidence and linkage disequilibrium (LD) structure, we have curated and narrowed down the list of the most likely candidate causal variants for each region. Functional annotation using data from ENCODE filtered for PrCa cell lines and eQTL analysis demonstrated significant enrichment for overlap with bio-features within this set. By incorporating the novel risk variants identified here alongside the refined data for existing association signals, we estimate that these loci now explain ∼38.9% of the familial relative risk of PrCa, an 8.9% improvement over the previously reported GWAS tag SNPs. This suggests that a significant fraction of the heritability of PrCa may have been hidden during the discovery phase of GWAS, in particular due to the presence of multiple independent signals within the same regio